baron brogaard kirilenko

7/30/2019 Baron Brogaard Kirilenko

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The Trading Profits of High Frequency Traders*

Matthew Baron

Jonathan Brogaard

Andrei Kirilenko

First Draft: October 2011

Current Draft: November 2012

Abstract: We examine the profitability of high frequency traders (HFTs). Using transaction level datawith user identifications, we find that high frequency trading (HFT) is highly profitable: HFTscollectively earn over $23 million in trading profits in the E-mini S&P 500 futures contract during themonth of August 2010. The profits of HFTs are mainly derived from Opportunistic traders, but alsofrom Fundamental (institutional) traders, Small (retail) traders, and Non-HFT Market Makers. WhileHFTs bear some risk, they generate unusually high average Sharpe ratios with a median of 4.5 acrossfirms in August 2010. Finally, HFTs profits are persistent, new entrants have a higher propensity tounderperform and exit, and the fastest firms (in absolute and in relative terms) earn the highest profits.

*Contact: Matthew Baron, Princeton University, (Email) [email protected], Jonathan Brogaard, FosterSchool of Business, University of Washington, (Email) [email protected], Andrei Kirilenko Commodity Futures

Trading Commission (CFTC), (Email) [email protected]. The views expressed in this paper are those of theauthors and do not represent the official position of the CFTC, its Commissioners or staff. Matthew Baron andJonathan Brogaard acknowledge funding from the CFTC. We thank Hank Bessembinder, Tarun Chordia, RichardHaynes, Charles Jones, Norris Larrymore, Wei Xiong, and Ryan Riordan for their valuable feedback, and theseminar participants at the Bank of Canada Market Microstructure Conference, Blackrock, the CFTC,Northwestern University, Princeton University, and the University of Washington for helpful comments.
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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I. IntroductionIn financial markets speed matters, whether using expedited information to make an investment

or being able to quickly enter trades. A new phrase, high frequency trading (HFT; or HFTs for high

frequency traders), has been used to identify a strategy that relies crucially on speed. HFTs have

surpassed floor traders as being the quickest to access markets, respond to changes in market

conditions, and intermediate trades. The time scale of such activities can be measured at microsecond

time frames, with position holding periods of mere seconds. Whether it is using expedited information

to make an investment, reduce risk, or mitigate the costs of adverse selection, those quickest to react to

information can best intermediate trading and capture informational rents.

In this paper, we examine the link between HFT speed, liquidity provision, and trading profits.

We have four main findings. First, HFTs are profitable, especially Aggressive (liquidity-taking) HFTs,

and generate high Sharpe ratios. Second, HFTs generate their profits from all other market

participants, and do so mainly in the short and medium run (seconds to minutes). Third, firm

concentration in the HFT industry is not decreasing over time, nor is its profitability. We conjecture

this is tied to our fourth finding that HFTs profits are persistent, new entrants have a higher propensity

to underperform and exit, and the fastest firms (in absolute and in relative terms) make up the upper

tail of performance.

We start by describing several stylized facts about the profitability of the HFT industry and the

distribution of profits across firms. We find that an important determinant of profitability is the level of

liquidity provision of a HFT firm. We find that the aggressiveness of a given HFT firm is highly

persistent not only across days but over a two-year span, and use this finding to classify HFTs into three

categories based on liquidity provision: Aggressive HFTs (if >60% of their trades are liquidity taking),

Mixed (if between 20% and 60% of their trades are liquidity taking), and Passive (if


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profits in August 2010, while Mixed and Passive HFTs earn significantly less: only $19,466 and $2,461

per day, respectively.

These stylized facts mask a wide dispersion of profitability on the individual account level, in

particular that the distribution of profits is highly concentrated toward a small number of firms, in

particular towards Aggressive HFTs. Furthermore, we find that the distribution of total profits across

HFT firms is widest within the Aggressive HFT category, with profits highly concentrated toward a

small number of these firms; in contrast, Passive HFTs have less dispersion and lower profits. While

HFTs bear some risk, they generate unusually high average Sharpe ratios in the range of 3 to 20, with a

median of 4.5 across firms in August 2010.

Next we study how HFTs generate these profits. We decompose traders profits by their trading

partners. We find that HFT firms profits are mainly derived from Opportunistic traders, but also to a

smaller extent from Fundamental (institutional) traders, Small (retail) traders, and Non-HFT Market

Makers. Second, we perform a spectral analysis on HFT firms profits. We find that Aggressive HFTs

make profits mainly on positions that they hold in the 1,000 100,000 transactions range, while Mixed

and Passive HFTs lose money in this range but earn profits in the very-short term (the 1 1,000

transactions range), perhaps reflecting the capturing of the bid-ask spread.

We evaluate further by considering the performance of individual firms. While the earlier

results show that HFTs on average outperform, the results do not track a single HFT firm. It could be

that while HFTs as a whole outperform, each particular HFT firms profits are random. We test for

persistence in profits at the firm level. We find that a firms profits yesterday positively predict its

profits today, in addition to its profits even months later. Persistent profits over time suggest that

something other than luck is driving a firms performance. Persistent performance may lead to

concentration as strongly performing firms will continue to perform well, but less successful firms will

exit the industry.

Next we analyze the profitability of new entrants and find they are not as profitable as existing

firms. In addition, they have a higher probability of exiting the market. Something other than chance


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could drive higher profitability of established firms relative to entrants. A small competitive advantage

early on, perhaps from experience (as in Seru, Shumway, and Stoffman, 2010) or ability, could

determine whether an HFT firm can consistently invest in ever more sophisticated technology and thus

maintain a competitive advantage over rival firms. Alternatively, the higher profitability of established

HFTs could be due to a survivorship bias: profitable firms remain while unprofitable firms exit; this

process of selection results in established firms having a higher average profitability than entrants, who

have not been selected out.

HFT profits exhibit large positive outliers some firms strongly outperform. Why might the

HFT industry exhibit this winners-take-all type concentration? A contributing factor may be speed.

The fastest firm may be able to consistently enter and exit more favorable trading opportunities or

cancel resting limit orders before they are picked off by faster traders. We measure both absolute speed

and relative speed and show that speed does matter. Absolute Speed matters for Mixed HFTs and

relative speed matters for Aggressive HFTs. For Aggressive HFTs competition for ever-increasing speed

creates a positional externality (Frank, 2005), since attempting to be the fastest seems to come at the

expense of other firms. While such an arms race, or rank-order tournament, can sometimes be socially

positive such as by incentivizing effort in situations where effort cannot be directly observed (Lazear

and Rosen, 1981) in the case of HFT, the positional externality may lead to a wasteful investment in

technology and human capital. The inherent problems with an arms race for ever-increasing speed and

technological sophistication thus raises questions about whether the speed of information

incorporation into the market at the millisecond time horizon has social value.

This paper contributes mainly to two literatures: the growing body of work on HFT and the

study of profitability by different groups of traders. In the first instance, researchers studying HFT must

overcome data limitations. No publicly available dataset allows researchers to directly identify HFTs.

Hasbrouck and Saar (2010) overcome this difficulty by using NASDAQ Total-ITCH order book runs,

messages in the order book that change rapidly (in milliseconds) and interact with each other. They

argue this activity comes from HFTs given the frequency of observations. However, with the Total-ITCH


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data it is not possible to rule out that these runs are coming from several anonymous slower traders or

an institutional market participant using an algorithm to enter a position. Moreover, the public order

book approach cannot be used to study HFTs' aggressive activity or the activity of individual firms.

A second approach to researching HFT has been to look at a small number of manually picked

firms that appear to be HFT firms. This is done in the NASDAQ data set used in Brogaard, Hendershott,

and Riordan (2011).1 NASDAQ, with the assistance of Terrence Hendershott, designated 26 firms as

HFTs and provided order book and trade data indicating activity by the 26 firms for 2008, 2009, and

part of 2010. While valuable for understanding HFT on NASDAQ, given the fragmentation of securities

trading, such data encompasses just a fraction of the total trading activity of HFTs in a given stock.2

We overcome these problems by taking an approach similar to Kirilenko, Kyle, Samadi, and

Tuzun (2010) who define different trading groups based on a selection criteria. HFTs are identified as

those firms with high volume, low intraday inventory and low overnight inventory. Like Kirilenko et al.

(2010), we are able to cleanly identify trading firms as HFTs based on a well-defined selection

algorithm described in the Data section. While all work done to date considers HFT to be a single type

of trading activity, we show the wide heterogeneity of trading strategies, profits, and speed within the E-

mini market. The data used in this paper consist of all the trades from the leading month contract of the

E-mini S&P 500 futures contract from August 2010 to August 2012. 3 Our data allow us to study the

strategies and profitability of HFT firms both cross-sectionally and in time-series over a two-year span.

One limitation of the paper is that our profit calculations do not account for all the costs of an

HFT firm. While we know the cost of exchange fees per contract ($0.15), direct data feeds, and co-

located servers, we cannot adequately calculate other costs such as computer systems, labor, and risk

management systems. We report gross trading profits throughout to limit speculative assumptions from

influencing our findings.

1 Hendershott and Riordan (2009) use a similar approach to categorize German DAX algorithmic traders;Hendershott, Jones, and Menkveld (2011) do the same for the NYSE.2 Menkveld (2011) studies one HFT, which seems to fit the HFT designation criteria used in this paper.3 We exclude the four months a year in which the leading contract expires in order to exclude rollover effects


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The focus of this paper is the profitability of HFTs. A number of previous studies have looked

into the profitability of different types of traders. For example, Harris and Schultz (1998) study the

profitability of SOES bandits, a group of individual traders in the 1990s who would quickly enter and

exit trades. They find SOES bandits on average earn a small profit per contract and that they do so over

several hundreds of trades per day. HFTs also aim to trade often, thousands of times per day, and earn a

small amount per trade. We find they earn $0.25 on average per contract traded. This equates to

$18,799 per day for each HFT in the August 2010 E-mini S&P 500 contract alone. Unlike mutual funds

(Carhart, 1997), but consistent with some of the literature on hedge funds (Jagannathan, Malakhov, and

Novikov, 2010), HFTs consistently outperform the market.

HFTs act as short-term intermediaries, and competition among such intermediaries is a widely-

used assumption in the market microstructure literature. This assumption is typically implemented as a

zero economic profits condition for market intermediaries (Easley and OHara, 1987; Glosten and

Milgrom, 1985; Kyle, 1985). Our findings question whether models built with zero-profit intermediaries

capture important strategic interactions in high-frequency markets.

Previous studies have also documented that different types of traders often engage in different

trading strategies. Like Ackermann, McEnally, and Ravenscraft (1999), who study the profitability of

different hedge fund strategies, we study different trading strategies of HFTs. While other studies look

into factors that induce different traders to trade (e.g. Grinblatt and Keloharju, 2001), we focus on

different market conditions and firm characteristics that drive firms to be profitable and look at how the

distribution of profits evolves over time.

The rest of the paper is as follows. Section II describes the data. Section III examines the

profitability of HFTs. Section IV studies how HFTs earn their profits. Section V studies market

concentration and entry/exit of firms within the HFT sector and Section VI concludes.

II. Data


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We use transaction-level data for the E-mini S&P 500 futures contract from August 2010 to

August 2012. We only look at the front-month contract for each month - the contract with the nearest

expiration date - which almost always has the highest volume and open interest of all open contracts,

and exclude months in which the leading contract expires in order to exclude rollover effects. For select

cross sectional analysis we focus on August 2010, which has a September 2010 expiration. For the rest

of the analysis we look at the months from August 2010 to August 2012 (excluding the expiration

months).

The data are trade-by-trade and contain common fields such as price, the number of contracts

traded, and time of the trade in units of seconds (and in milliseconds for a few of the months we

examine). In addition, the data contain a variable identifying the buyer and seller at the user-level and

identifies which side initiated the trade. The data also allow us to group multiple transactions into an

order. That is, if there is a market order for 10 contracts and three different market participants provide

liquidity for the trade, we can observe the three different liquidity providers matched to the single

trader's executable order, as well as determine that they were all related to one order.

Cancelled transactions and other irregular transactions can also be identified in our dataset and

have been filtered out. Each contract has a multiplier of $50 times the value of the underlying S&P 500

index; thus a contract with an index value of 1000 indicates the futures contract is valued at $50,000.

The tick size in the S&P 500 E-mini is .25 index points; thus, given the $50 multiplier, a one tick change

is equivalent to $12.50. The contract is cash-settled against the value of the underlying S&P 500 index.

The dollar value of trading volume is approximately $200 billion per day in August 2010.

The S&P 500 E-mini is a favorable setting for studying HFT as it is a highly liquid market with

several different market participants regularly trading, including a high number of HFTs. Hasbrouck

(2003) shows that the E-mini futures contract is the largest contributor to the price discovery process of


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the S&P 500 index. In addition, because the contract only trades on the Chicago Mercantile Exchange,

there is no concern about unobserved trades occurring on other exchanges.4

In addition, only minimal requirements prevent entities from engaging in HFT and a HFT firms

operating costs are relatively low.5 Given the low obstructions to participate as an intermediary in the E-

mini market and the low costs to set up a HFT operation, we should find a market in which competitive

forces drive down profits. The E-mini market has no designated market makers, no liquidity rebates,

and no obligations for market participants (such as making prices continuous). There are no

institutional barriers to entry to become an intermediary in this market and no duty to undertake

trades, so that HFT trading activity is presumably in explicit pursuit of profits. The E-mini trading

environment provides an appealing setting to test the efficiency of markets at the sub-second time

interval.

The Globex matching engine stamps a unique matching ID on each transaction, which identifies

the exact ordering of transactions. The contract is in zero net supply and buying and selling are

symmetrical, so there are no short-selling constraints. Initial margins for speculators and hedgers

(members) are $5,625 and $4,500, respectively, in August 2010; maintenance margins for all traders

are $4,500. While the S&P E-mini futures contract trades almost continuously, we only use data during

normal trading hours: 8:30 a.m. - 3:15 p.m. Central Standard Time.6 Finally, trading in the E-mini is a

zero-sum gain: one traders profits come directly at the expense of another trader.

a. Categorizing TradersThe categorization of traders used in this paper is based on capturing the common

characteristics of a high frequency trader: a market participant who trades a large number of contracts,

4 Note that unlike many equity markets, the E-mini S&P 500 futures market does not have maker-taker fees for thefront month contract.5 Such costs include co-located servers, data feeds, and exchange fees.6 The E-mini market only occurs on electronic markets. There is a short break in trading between 4:30 p.m. and 5:00p.m. Central Standard Time.


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consistently maintains a low inventory level, and ends the day at or near a zero inventory position. We

find 65 firms satisfy the HFT criteria in August 2010 and a similar number in the other months studied.

The precise selection criteria are as follows. For each month, there are three categories a

potential trader must satisfy to be considered a HFT: (1) Trade more than a median of 5,000 contracts

in all the days that this trader is active; (2) have a median (across days) end-of-day inventory position,

scaled by total contracts the firm traded that day, of no more than 5%; (3) have a median (across days)

maximum variation in inventory that day (maximum position minus minimum position that day),

scaled by total contracts the firm traded that day, of less than 10%.

We create three different subcategories of HFTs based on their aggressiveness, noting that the

aggressiveness of a given HFT firm is highly persistent across days. The subcategories are Aggressive,

Mixed, and Passive. The definition is based on how frequently the HFT firm initiates a transaction. To

be considered an Aggressive HFT, a firm must meet the previously-discussed HFT requirements and

must also initiate at least 60% of the trades it enters into; to be considered a Passive HFT a firm must

initiate fewer than 20% of the trades it enters into; those HFTs that meet neither the Aggressive nor the

Passive definition are labeled as Mixed HFTs. There are 14 Aggressive, 30 Mixed, and 21 Passive HFTs

in August 2010 and similar numbers in the other months.

We classify non-HFT firms into four different subcategories: Non-HFT Market Maker,

Fundamental, Small, and Opportunistic traders. We define a Non-HFT Market Maker as any non-HFT

firm that in a particular month: (1) Provides liquidity in at least 80% of the trades it enters into; (2) has

a median (across days) end-of-day inventory position, scaled by total contracts the firm traded that day

of no more than 15%; and (3) trades a median of at least 20 contracts per day. We identify 737 Non-

HFT Market Makers in our sample for the month of August 2010. The Non-HFT Market Maker

category captures traditional market makers examined by Hasbrouck (1993) and Coughenour and Saad

(2004).

Next, we define Fundamental traders and Small traders. The Fundamental trader category is

meant to capture institutional traders (e.g. Anand, Irvine, Puckett, and Venkataraman, 2012; Puckett


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and Yan, 2011) while the Small trader category is more like retail traders (e.g. Kaniel, Saar, and Titman,

2008; Seasholes and Zhu, 2010). A Fundamental trader is defined as any firm which: (1) Trades a

median of at least 1000 contracts per day (about $60 million in notional value); and (2) has a median

(across days) end-of-day inventory position divided by total contracts the firm traded that day greater

than 30%. Such firms generally represent traders who are interested in taking large directional

positions and holding them overnight. There are 346 firms classified as Fundamental traders in August

2010.

Small traders are defined as firms that trade less than a median of 20 contracts a day of all the

days that firm is active. This is the majority of traders, with 21,761 participants in August 2010. The

remaining firms do not fit in the specified categories and are therefore grouped into the Opportunistic

category. There are 8,494 such firms in August 2010. Traders in the Opportunistic category thus are

medium-sized traders who either take large directional positions (but are not large enough to be

classified as Fundamental traders) or who move in and out of positions throughout the day but with

significantly larger fluctuations and persistence in their positions than HFTs and Non-HFT Market

Makers. This group likely captures brokerage firms, hedgers, small institutional investors, hedge funds,

and other hard-to-identify traders.

b. Summary StatisticsTable 1 presents a summary of trading behavior for these different trader types for August 2010.

INSERT TABLE 1 ABOUT HERE

For each trader type, four statistics are reported: The daily percent of market volume traded, the

daily percent of liquidity-taking contracts (aggressive contracts by trader category / total market

volume), the daily aggressiveness ratios (aggressive contracts by trader category / total contracts by

trader category), and the average trade size per transaction.


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Table 1 Row 8 shows that, on average, 3.2 million contracts are traded in the S&P 500 E-mini

per day. This is a liquid market with on average about 70 contracts trading every second. HFTs as a

whole trade 54.4% of the double-counted trading volume

MktVolume

SellsBuys HFTHFT

*2

, or 1.73 million

contracts daily (Row 1+2+3). The next largest category is Opportunistic, with 31.93% of contract volume

by its 8,494 participants (Row 7). The variation within the HFT categories over different days is

considerable. For example, Aggressive HFTs range from 9.5% to 17.8% of market volume across days;

they have the largest variation of the three HFT categories (Row 1).

Passive HFTs make up a significantly smaller portion of HFT volume (8.87%, Row 3) than

Aggressive HFTs (15.22%, Row 1). The contrast between the HFT types is stark: for example, Aggressive

HFTs take 25.60% of market liquidity (Row 9), while Passive HFTs take only 2.19% (Row 11). In terms

of their respective aggressiveness, that equates to Aggressive HFTs taking liquidity in 84.22% (Row 17)

of the contracts they trade and Passive HFTs only taking liquidity in 12.35% (Row 19). The trade size

between the categories also varies substantially: Aggressive HFTs average trade size is 5.3 contracts

(Row 25), compared to 2.3 for Passive HFTs (Row 27). The non-HFT categories also have a great deal of

variation, with Fundamental traders having a 5.67 average trade size (Row 28) compared to Non-HFT

Market Makers 3.92 (Row 29).

Next, we turn to examining volume and positions of the different trader types across the two-

year span. Figure 1, Panel A shows the average daily HFT volume of the HFT subgroups. The total

market volume decreases over the two-year span from 3,187,011 contracts in August 2010 to 2,322,787

in August 2012. About half of that decline was from a reduction in Mixed HFT trading from 960,643

contracts in August 2010 to 564,200 contracts in August 2012, while Aggressive and Passive HFT

volume was relatively constant.

INSERT FIGURE 1 ABOUT HERE


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Figure 1, Panel B looks at what percent of market volume each trader type comprises for the two

year span. Surprisingly, although average daily market volume fluctuates considerably over the two-

year span, from a high of over 3 million contracts in August 2011 to a low of 2,322,787 contracts in

August 2012, the percent traded by each type is relatively stable. For example, HFT percentage volume

starts in August 2010 at 54.37% and ends in August 2012 at 55.53%; similarly, Opportunistic percentage

volume starts in August 2010 at 31.93% and ends in August 2012 at 30.30%. However, Aggressive HFT

volume increases over the two years from 15.22% to 22.63%, while Mixed HFT volume decreases from

30.28% to 24.59%.7

Taken together, Figure 1 Panels A and B contradict the common assumption that HFT volume,

both in absolute terms and as a percentage of the market, has been increasing in recent years; in the E-

mini S&P 500 futures contract, it is in fact decreasing in absolute terms and holding relatively constant

in percentage terms.

Figure 1 Panels C and D report the inventory dynamics of the three different types of HFTs.

Panel C shows absolute value of end-of-day positions, first taking the median across trading days for

each firm individually and then averaging across all HFT firms within each type. Panel C shows that

HFTs carry little overnight positional risk by zeroing out their inventories at the end of each trading

day: in our two-year sample, Aggressive HFTs carry an average of 25 contracts overnight, Mixed carry

an average of 6 contracts overnight, and Passive HFTs carry an average of 5 contracts overnight.

Beyond managing end-of-day inventory, HFTs limit the positions they take intraday. Panel D

reports average inventory range, defined as the maximum position taken on a day minus the minimum

position taken on that same day, first taking the median across trading days for each firm individually

and then averaging across all HFT firms within each type. Panel D shows that HFTs trade within

modest inventory bounds: in our two-year sample, Aggressive HFTs carry an average intraday range of

7This is not due to Mixed HFTs changing categories to Aggressive HFTs; in fact, no HFT that started off as Mixed or Passive

changed to Aggressive during the two year span.


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737 contracts, Mixed carry an average intraday range of 388 contracts, and Passive HFTs carry an

average intraday range of 208 contracts.

III. The Profitability of High Frequency Traders

We document four key aspects of profitability. First focusing on HFT profits during August

2010, HFT profits vary across firms and across days. Aggressive HFTs have a right skew and large

kurtosis. Second, a simple model demonstrates that the probability of default by a HFT firm is quite

small. Third, HFT profits are level over the two-year span. Finally, the risk and return tradeoff of HFT

firms using the Sharpe ratio shows that they generate large returns given the risk they undertake.

a. Distribution of Profits in August 2010Throughout the paper, daily profits for each firm, i, is calculated for each trading day, t,

according to marked-to-market accounting, assuming that each trader starts each day with a zero

inventory position. More precisely, for each trader, we calculate the end-of-day profits as the

cumulative cash received from selling short positions minus the cash paid from buying long positions,

plus the value of any outstanding positions at the end-of-day, marked to the market price at close:

TiN

n

TiTninti ypyp,

1

,,, , (1)


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where n=1...Ni,T indexes the trades for trader ibetween the start of the trading day (t=0) and the

end of the trading day (t=T),ps is the price of the trade, yi,n is the quantity of the n-th trade by trader i,

andpTyi,T is the value of any end-of-day positions outstanding.8

Table 2 analyzes the distribution of profits for August 2010. Each observation in this table is a

daily profit of a single HFT account (firm-day observations with trading quantity less than 1000 were

removed). Summary statistics such as mean, median, skew, and kurtosis are reported here for both

profit and profit-per-contract, in addition to total monthly profits, maximum daily loss of a firm, and

maximum daily loss scaled by the average daily profit of that firm.


Aggressive HFTs earn a mean of $45,267 in gross trading profits in August 2010 (Column 2),

while Mixed and Passive HFTs earn significantly less: only $19,466 and $2,460 per day, respectively.

The P-value on the statistical significance of profits (Column 7) shows that these values differ

statistically from zero. While the averages are all positive, there is a wide distribution of profitability.

The standard deviation of the profits (Column 4) has Mixed HFTs realizing the highest variation in

profits ($273,240) and Passive HFTs the lowest ($46,638). The skewness and kurtosis (Columns 5 and

6) statistics show that the distribution of profits is non-normal. There is excess weight in the tails, in the

upper tail especially, for Aggressive HFTs (positive skew) and in the lower tail for Mixed and Aggressive

HFTs (negative skew). Additional data are reported in Panel A to emphasize the profit and risk of HFT.

Column 8, Total Monthly Profits, shows the overall profits during August 2010 for the HFTs. The HFTs

in August 2010 earn an aggregate of $23.6 million dollars in gross trading profits.9 Annualized, this

corresponds to a profit of over $280 million.

8 As Figure 1 Panel C shows, HFTs end the day near a zero inventory and so marking-to-market at the end of thetrading day is relatively innocuous.9 We also calculate the total profits for 24-hour continuous trading (as opposed to looking only at regular tradinghours) and find qualitatively similar results for the three subtypes of HFTs.


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The lower part of the table reports the distribution of profits per contract. It generally has the

same conclusion as the level of profitability results in Panel A: Passive HFTs are the least profitable of

the HFT types.

The profits HFTs earn are not risk free. Columns 9 and 10 emphasize the losses HFTs can incur.

Column 9, Maximum Loss, is the largest loss any HFT experiences on a day. Column 10,Max Loss per

Average Profit, is the largest loss an HFT realizes (averaged across traders), scaled by that firms

average daily profit. The table shows that Mixed HFTs can lose over two million dollars in a single day,

and the maximum loss is half a million for both Aggressive and Passive HFTs (Column 9). Across all

HFTs, the maximum loss per average profit is less for Aggressive HFTs than for Mixed and Passive

HFTs. Aggressive HFTs can expect to have days where they lose $1.55 per dollar of average profit,

whereas Mixed HFTs have days were they realize losses of $35.02 per dollar of average profit (Column

10).

The fact that Aggressive HFTs earn substantially higher profits than Passive HFTs suggests

there is a strong profit motive for liquidity taking rather than liquidity providing. The existence and

high profitability of Aggressive HFTs shows that, while on average HFTs are liquidity providers, many

are not.

b. Probability of DefaultWhile HFT strategies are highly profitable, they are also risky on a day-to-day basis. As

discussed above in Table 2, Panel A, the average daily profit for a given Aggressive HFT is $45,267 but

the standard deviation is $167,411, almost four times the average. Thus, while it is possible for HFTs to

earn substantial daily profits, it is also possible to lose large amounts. In Table 2, we see that Mixed

HFTs even lose over two million dollars in a single day, and the maximum loss is half a million for both

Aggressive and Passive HFTs.


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However, simple calculations show that the downside risk for a HFT firm is quite negligible,

despite the seemingly large standard deviation of daily profits. For example, if daily profits are

independent and identically distributed and normally distributed with mean = $45,000 and standard

deviation = $170,000, similar to what we find in Table 2, 10 and if each trader has initial capital, V0 =

$10 million that it can deploy on any given day11, we can model the evolution of a trader's net worth as

an arithmetic Brownian motion with constant drift and constant volatility . Given that the trader has

V0 = $10 million net worth at time 0, based on the theory of hitting times we can calculate the

probability that the trader defaults at any finite time (i.e. Vt = 0) by the formula

(Karlin and Taylor, 1975 p. 361). Calibrating the formula to the values of, 2, and V0 that

we observe in the dataset, we find that P(default) < 0.0001. The trader's probability of defaulting is

virtually zero. Also, simple calculations using the normal distribution show that the probability of an

HFT at least breaking even (at $10 million) after a year (252 trading days) is >99.9%, and the

probability of an HFT at least doubling its initial capital after a year is about 69.0%.

c. HFT Profits over Time

We look at average daily HFT profits and profits per contract over the two-year span. To

motivate the magnitude and distribution of HFT profits, we present Figure 2 which shows for each

month the distribution of average daily profits (Panel A) and average daily profit per contract (Panel B)

across firms. Figure 2 shows the time-series of average daily HFT profits (Panel A) and profits per

contract (Panel B), broken down into Aggressive, Mixed, and Passive groups and with all firms

aggregated together in their respective groups.


10 These assumptions are approximately true. We construct an autocorrelogram across days which shows that thecorrelation decays rapidly (results available upon request).11 We can infer the initial capital based on the fact that the average HFT has a maximum inventory band of about 200contacts, which valued at approximately $50,000 each, comes to $10 million. The $10 million assumes fully capitalizedpositions.


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Table 2, Panels B and C report the time series of profits. Panel B shows the monthly aggregate

mean profitability per HFT firm, the standard deviation, the P-value of the mean, and the P-value of the

median. Panel C reports the same but for the mean profitability per contract traded. The results are

divided into groups based on the three subgroups of HFT, Aggressive, Mixed, and Passive.

The average monthly profits of HFTs vary substantially. Aggressive HFTs consistently earn

positive average daily profit over the two-year span, with a mean of $395,875 per day over the two-year

span, and with a high of $2,745,724 per day in August 2011 and a low of -$86,296 in January 2012;

Mixed HFTs earn an even higher positive average daily profit over the two-year span (because there are

more firms, even though each firm individually makes less), with a mean of $525,064 per day over the

two-year span, and with a high of $890,828 per day in October 2010 and a low of $63,027 in January

2011; and Passive HFTs earn the lowest but still positive average daily profit over the two-year span,

with a mean of $107,239 per day over the two-year span, and with a high of $403,259 per day in

January 2012 and a low of -$22,499 in February 2011.

Panel C shows the time-series of total monthly profits divided by total monthly contracts traded.

Aggressive HFTs earn the highest average daily profits per contract over the two-year span, with a mean

of $0.85 over the two-year span, and with a high of $2.01 in May 2011 and a low of $0.09 in January

2012; Mixed HFTs earn a less but still positive average daily profit per contract over the two-year span,

with a mean of $0.52 per day over the two-year span, and with a high of $0.93 in May 2011 and a low of

-$0.23 in January 2011; and Passive HFTs earn the lowest but still positive average daily profit per

contract over the two-year span, with a mean of $0.46 over the two-year span, and with a high of $1.18

in January 2012 and a low of -$0.47 in February 2011.

Figure 3, plots the average daily profits of firms at the 10 th, 25th, 50th, 75th and 90th percentiles.

Each panel is broken down into three graphs for Aggressive, Mixed and Passive HFTs.



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Performing a simple t-test on whether there is a mean difference between the average firm profit

in August 2010 and August 2012 we find that Mixed HFTs have had no statistically significant change in

their profits, while Aggressive and Passive HFTs have actually increased (P-value of .08 and .03,

respectively). On a per contract basis, the same is true: Mixed HFT profits have remained the same, but

Aggressive and Passive HFTs have experienced an increase (P-value of .08 for both).

d. Risk and ReturnTrading profits provide insight into the magnitude of HFTs' profits, but the variable of interest

to financial economists is risk-adjusted performance. In an efficient market, returns above the risk-free

rate should be proportional to risk. It may be that while the profits are high, the risks associated with

generating them are also high, and so the risk adjusted returns are average or low. Next, we analyze this

possibility.

We evaluate the Sharpe ratios of HFTs (Sharpe, 1966). The Sharpe ratio for each trader is

calculated as:

252*

,

,i

fti

ti

rr

SR

, (2)

where ri,t is the average daily return for trader i, calculated from the daily profit for trader iand

assuming the maximum inventory dollar value of trader i is the amount of investable capital. is the

standard deviation of trader i's returns over the sample period.12

In Figure 4, we examine the Sharpe ratios of Aggressive, Mixed, and Passive HFTs, calculated by

looking at daily returns. Menkveld (2011) calculates the Sharpe ratio of an HFT firms trading in

equities markets to be 9.35. Similarly, we find that on average Mixed HFTs have the highest risk-return

tradeoff, generating a Sharpe ratio of over 10.46. Passive HFTs generate a Sharpe ratio of 8.56, and

12 The risk-free rate is not subtracted from r as is normal because the time horizon is so short and the rate duringAugust 2010 to August 2012 was so low as to make it an inconsequential value. The Effective Fed Funds Rate inAugust 2010 was 0.19% (research.stlouisfed.org).


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Aggressive HFTs 8.46. Yet even within these different types of HFTs, the Sharpe ratio for firms varies

widely for example, 25% of Mixed HFTs have a Sharpe ratio greater than 17.11. The Sharpe ratios and

their distributions are reported graphically in Figure 4.


The risk-adjusted performance of the median Aggressive or Mixed HFT firm is 12 times higher

than the Sharpe ratio of the S&P 500 (0.31) (Fama and French, 2002). The distribution is wide, with

standard deviation of 10.0, 11.5, and 7.1 for Aggressive, Mixed, and Passive HFTs, respectively, in

August 2012. Sharpe ratios at the top 10 th percentile are 21.5, 19.3, and 12.7 for Aggressive, Mixed, and

Passive HFTs, respectively, meaning that a subset of firms achieves risk-adjusted performance 40 to 70

times that of the S&P 500.We thus conclude that while HFTs bear some risk, their risk-adjusted

returns are unusually high.

IV. How do HFTs Make Profits?

Section III documents that HFTs earn high risk-adjusted returns, and they do not appear to be

decreasing over time. Before exploring in detail these facts we further explore how HFTs earn these

profits. We begin by tabulating the counterparties from which HFTs earn their profits to determine

from whom HFTs earn their profits. Next we perform spectral analysis of the profits to analyze the

time-scale over which HFTs earn their profits.

a. HFT Profits by Counterparty


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From whom do these profits come? In addition to HFTs, we divide the remaining universe of

traders in the E-mini market into four categories of traders: Fundamental traders (likely institutional

traders), Non-HFT Market Makers, Small traders (likely retail traders), and Opportunistic traders. We

decompose what we call short-term profits into how much each category is earning from the others. As

we will see, HFTs earn most of their profits from Opportunistic traders, but also earn profits from

Fundamental traders, Small traders, and Non-HFT Market Makers. Small traders in particular suffer

the highest short-term losses to HFTs on a per contract basis: $3.49 per contract to Aggressive HFTs

compared to $1.92 for Fundamental traders and $2.49 for Opportunistic traders, for a contract valued

at approximately $50,000.

Table 3 breaks down the trading profits by trading pairs in August 2010: the rows identify who

receives the profits, whereas the different columns represent from whom the profits are derived.

Fundamental traders capture institutional investors, who are generally considered informed (e.g.

Badrinath, Kale, and Noe, 1995; Boehmer and Wu, 2008; Boulatov, Hendershott, and Livdan, 2011;

Hendershott, Livdan, and Schurhoff, 2012). Under the informed trader hypothesis we expect to see

HFT profits being small, or even negative, when trading with Fundamental traders. However, a growing

literature shows that Fundamental traders may trade in a way that makes their order flow noticeable

(Hirschey, 2011). Heston, Korajczyk, and Sadka (2010) show that institutional traders leave a detectable

pattern in their trading activity. Under the detectable patterns hypothesis we would expect HFT profits

to be higher when trading with Fundamental traders than with others.

We have the opposite hypotheses for Small traders (retail investors). Retail investors are

thought to be noise traders and so under the uninformed hypothesis we expect them to incur significant

losses to HFTs (e.g. Hvidkjaer, 2008; Kaniel, Saar, and Titman, 2008; Barber, Odean, and Zhu, 2009).

However, because retail traders are small and trade noisily they may not leave patterns in the data (due

to their one-off orders) and consequently HFTs may have a more difficult time inferring information


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from the small traders order flow. Under the undetectable patterns hypothesis we would expect Small

firms to lose less to HFTs.

Whether HFTs will make profits from Non-HFT Market Makers is an empirical question: HFTs,

especially Passive HFTs, compete for order flow with Non-HFT Market Makers. Thus, on balance, we

do not expect that Passive HFTs earn profits by trading with Non-HFT Market Makers. However,

Aggressive HFTs may earn profits from Non-HFT Market Makers by picking off stale quotes.

We construct Table 3 by considering only the trades in August 2010 between two groups and

calculating the profit flows that result from those trades. To illustrate, we calculate the Aggressive HFT-

Fundamental profit flows by removing all trades except those for which one party was an Aggressive

HFT and the other party was a Fundamental trader. We do not take into account which of the two

parties is the buyer or seller, or which is the aggressive party. Based on the remaining trades, for each

day we calculate the daily profits for the HFTs and for Fundamental traders over the course of the

month.

The profits calculated in Table 3 are the implied short-term profits: we calculate the marked-to-

market profits of each trader on 1 minute frequencies and reset the inventory position of each trader to

zero after each of these 1 minute intervals. Then, we sum up all the 1 minute interval profits to get a

measure of daily profits. Therefore, we capture the short-term profits of traders and not gains and

losses from longer-term holdings. Since the futures market is a zero-sum game, the resulting profits

matrix is symmetrical and zero along the diagonals.13

Note that our focus is on returns during a short horizon. A loss during this interval does not

imply that the trader (or trader category) loses money overall. In addition, we only observe a market

participants activities in the E-mini market, which may be one of multiple markets in which a trader

participates. For instance, Fundamental traders may be using the E-mini contract as a hedge and

Opportunistic traders may be doing cross-market arbitrage. Thus, a loss in the E-mini market does not

imply the trading firm loses money overall.

13 A limitation of the approach taken in Table 3 is that it can only measure profits from direct order flow.


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On average Aggressive and Mixed HFTs make positive profits from all other types of traders,

while Passive HFTs make positive profits from all other types of traders except from Fundamental

traders. Row 2 of Panel A, Table 6 shows that on an average day, Aggressive HFTs (in aggregate) make

$1,691,738 from Fundamental investors, $1,962,675 from Non-HFT Market Makers, $379,275 from

Small traders, and $8,171,350 from Opportunistic traders. While Mixed HFTs make positive profits

from all other (non-HFT) trader types, they lose money to more aggressive HFTs. In particular, Mixed

HFTs lose money to Aggressive HFTs (Column 4, Row 4, $-7,190,140), and Passive HFTs lose money to

both Aggressive HFTs (Column 4, Row 5, $-2,557,038) and Mixed HFTs (Column 5, Row 4, $-

1,400,125).

Panel B of Table 3 expresses the trading profits between groups as a percentage of a groups total

profit.14 For example, Column 1, Row 2 is the percent of HFTs profit derived from trading with

Fundamental traders: Aggressive and Mixed HFTs earn 7.7% and 2.9% of their profits respectively from

trading with Fundamental traders. For groups that have net losses (Non-HFT Market Makers, Small

Trader, and Opportunistic), Panel B expresses the percent of total losses: For example Column 2, Row 5

shows that 68.7% of all Non-HFT Market Maker traders losses are from trades with Aggressive HFTs.

Row 1 of the table shows that Aggressive HFTs make most of their profits from trading with

Opportunistic (37.2%) and Mixed HFT (32.8%) market participants. Furthermore, the different sub-

types of HFTs make profits from each other. There is a hierarchy among the HFTs: Aggressive HFTs

earn profits from Mixed and Passive HFTs, while Mixed HFTs earn profits from Passive HFTs.

Lastly, Panel C describes the profits and losses on a per contract basis. These results provide an

estimate of the effective transaction costs involved in trading with certain groups. Since we compute

14 Note how each row sums to 100% when either only Column 2 (HFT) or Columns 3, 4, and 5 (the HFT types) areconsidered.


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profits on a 1 minute basis while resetting each traders inventory to zero, their profits can be

interpreted as short-term transaction costs extracted from the rest of the market, not gains from long-

term directional positions. For example, Fundamental traders incur a loss of -$1.92 (Column 2, Row 5)

when trading with Aggressive HFTs, while Small traders experience a much larger loss of -$3.49

(Column 2, Row 7). Interestingly, Small traders lose similar amounts per contract to non-HFT traders.

The empirical results support the first hypothesis that Fundamental (institutional) traders are generally

informed traders able to evade leaving a detectable pattern in their trading activity from which HFTs

glean information. The results also support the hypothesis that Small (retail) traders are noise traders

who incur the largest effective transaction costs per contract.

Column 9 reports the effective transaction cost imposed on all other traders. Since Aggressive

HFTs collect $2.04 per contract (Column 9, Row 2) over 15.2% of the volume (Table 1), while everyone

else loses while trading 84.8% (=100% - 15.2%) of the volume, the effective Aggressive HFT imposed

transaction cost on all other traders is $2.04*(0.152/0.848) = $0.36 per contract. Scaling this per-

contract transaction cost by $50,000 the approximate price of a contract yields an estimated HFT-

imposed transaction cost of 0.0007%.

b. Spectral AnalysisTo understand the investment horizon of HFTs, we follow Hasbrouck and Sofianos (1993) and

decompose HFT profits in August 2010 over different time horizons using spectral analysis. The time-

horizon over which HFTs make their profits provides insight into their trading strategies and allows us

to further examine the differences between the types of HFTs.

Spectral analysis treats marked-to-market profits as a function of two different time series:

prices and inventory levels, which can vary at different frequencies. Fourier analysis is used to

decompose prices and inventories into waves of varying frequencies: if the two time series, prices and

inventories, are in phase (traders buy before the price is going up) they make profits, while if the two

time series are out of phase (traders buy before the price goes down) they incur losses. We find that


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Aggressive HFTs as a whole lose money on shorter time scales (on round trip transactions that occur on

a time scale of a 1,000 or fewer total market transactions) but gain money on longer time scales, those

over 1,000 market transactions. In contrast, both Mixed and Passive HFTs tend to gain money at time

horizons of 1,000 transactions or fewer, and instead lose money over the longer intervals.

Spectral analysis must be conducted in transaction time, as opposed to clock time, as several

trades regularly occur within a second and, while we can order trades at the sub-second level, we are

unable to determine the time between trades within a second due to the precision of the time stamp

(second-by-second). Thus, our time variables t,, and T(defined below) refer to transaction time. There

are approximately 10 transactions per second.

Mathematically, we express mark-to-market profits for any individual trader at time as:

(3)

wherext is the inventory holdings of that trader and pt is the price at time t. Spectral analysis

requires us to assume that xt and pt are stationary processes, which is a valid assumption to make

given thatxt, HFT firms inventories, is a mean-reverting process andp, the first difference of the price

process, is a martingale difference sequence.

We define the following functions:

(4)

(5)

where the variable is interpreted as a wavelength having units of transaction time, and

and are the spectral densities of thextandpt, respectively.


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We can recover the original marked-to-markets profits formula in (3) using the following

formula. (See Hasbrouck and Sofianos, 1993 for details regarding Fourier analysis):

, (6)

whereRealis the function that takes the real part of a complex number. The last equality in Equation

(6) follows because the imaginary part of sums to 0. The term captures

the component of the marked-to-market profits generated at tradingwavelength .

We compute the spectral density of profits for each day and HFT firm using Equations (4)

through (6). For each firm-day we decompose the summation in Equation (6) into the following

intervals: 1-10, 11-100, 101-1,000, 1,001-10,000, 10,000-100,000, and 100,000+ market transactions.

This decomposes the total daily profit for each firm into different components based on the time-

horizon of the trading strategy. For each trader and each interval, we take the median profits over the

course of the 22 days in our August 2010 sample. For each of the three sub-types we take the median

and the 25th and 75th percentiles of profits across firms. The spectral analysis of profits results are

reported in Table 5.


Row 1 in Table 7 shows that in August 2010 Aggressive HFTs tend to make positive profits at

medium time scales, in the 1,001-10,000 and 10,001-100,000 transaction range (Columns 2 and 3),

with negative profits at short ranges (11-100 and 101-1,000 transaction intervals) and the longest time

scale of 100,000+ transactions (Column 4). In order for an aggressive trade to be profitable, a trader

must not only predict the direction of the price process but also overcome the bid-ask spread. We

suspect that this is the reason Aggressive HFTs fail to make money at the shortest time intervals. The


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spectral analysis results are consistent with the notion that Aggressive HFTs make money by

anticipating price movements in the 1,000 100,000 transactions range, while losing money at both

very short and long time scales.

In contrast, both Mixed and Passive HFTs tend to gain money at short time scales (1-10, 11-100,

and 101-1,000 transactions) while losing money on longer time scales (1,001-10,000, 10,001-100,000,

and 100,000+ transactions). These results are consistent with the idea that Mixed and Passive HFTs

earn the bid-ask spread in the short-run but are adversely selected on a longer time scale.

V. Market Concentration and Entry/Exit of HFT Firms

So far we have documented that HFTs earn above average profits given the risks they assume,

and we have analyzed the time horizon of holding and trading partners that contribute to these profits.

In this section we analyze entry and exit of HFTs into the HFT market. Our results indicate that the

industry lends itself to concentration. We first show that over time the Herfindahl index does not seem

to be decreasing. Next we provide evidence of firm-level persistence in profitability. Focusing on new

entrants, we find that new entrants at first perform in-line with other HFTs, eventually underperform

and have a higher probability of exiting. Finally, we show that a defining factor of HFT, speed, plays an

important role in determining the profitability of an HFT firm, particularly for Aggressive HFTs.

The Herfindahl index is a commonly used measure of concentration of market share or earnings

within an industry. Table 5 calculates the Herfindahl index for each sub-group of HFTs, for each month

in the data set.


We report a Profit-based Herfindahl index as well as a Volume-based one. The Profit Herfindahl index

is calculated as:


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[

]

(7)

whereNis the number of firms in the HFT subgroup in month t that earn non-negative profits,Profiti,t

is firm is total trading profits in month t, andHFT Profitt is the total trading profits of all HFT firms in

the HFT sub group of interest (Aggressive, Mixed, or Passive). The Volume Herfindahl is calculated

using the same formula but considering the number of contracts traded instead of trading profits. The

Herfindahl index has a range of (0,1].

A larger number implies a more concentrated industry, which is a proxy for the level of

competition in the industry. As a reference, Van Ness, Van Ness, and Warr (2005) find that market

makers have an average Herfindahl index (created with trading volume, instead of profit) on NASDAQ

of .14, with a range of .037 to .439. The results in Table 6 for both the Profit-based and Volume-based

number are in line with this range. Perhaps more interesting, however, than the level is the direction. A

simple univariate regression of the Profit based and Volume based Herfindahl indices on time shows

that concentration is not decreasing, and is increasing for Mixed and Passive HFTs. For both the Profits

and Volume based measures, Herfindahl index increases over time for Mixed HFT (significant at the

10% level for Profits, and the 1% level for Volume), decreases over time for Passive HFT (significant at

the 1% level for both), but is unchanged for Aggressive HFTs. HFT is a rather new industry, and so one

might expect concentration to decrease as new entrants join the market. We observe the opposite.

a. The Consistency of HFT ProfitsThe results in Section III show that both across time and across types, HFTs earn positive

profits. However, the results do not provide an insight into whether it is the same traders earning

profits over time. To examine the consistency at the individual firm level, we ask if HFTs that are

profitable one day continue to be profitable in subsequent days. As suggestive evidence we produce a

figure that addresses the question, Do HFT firms that outperformed or underperformed in August 2010


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continue to out- or under-perform during the subsequent two-year span? We find this to be the case for

Aggressive HFTs but not for Passive HFTs.


Figure 5 shows the average daily profitability of HFTs in the August 2010-based over- and

under-performing categories, in addition to all HFT firms. Within each of the three HFT types,

Aggressive, Mixed and Passive, HFTs that were in the top tercile of profit earners in August 2010 were

labeled Top 3rd, Those in the lowest tercilewhere labeled Bottom 3rd We trace out the average daily

profits of these groups and for all HFTs over the two-year span. The Figure shows whether firms that

start out outperforming/underperforming other HFTs continue to outperform/underperform.

For Aggressive and Mixed HFTs, those that outperform/underperform other HFTs in August

2010 continue to do so in the subsequent two year span (conditional on these firms staying in the

market). However, this is not true to Passive HFTs, demonstrating that outperforming or

underperforming other HFTs in August 2010 was due to chance. Interestingly, all the Aggressive and

Mixed HFTs in the bottom third exit the market by January 2012, and all the Passive HFTs in the

bottom third exit by April 2012.

To formally analyze the persistence of HFT profits we look at the role that yesterdays profits

have in predicting todays profits for an HFT. Persistent profits over time suggest that something other

than luck is driving a firms performance. Also, persistent performance may lead to concentration as

strong performing firms will continue to perform well, but less successful firms will exit the industry.

To test persistence we run the following OLS regression:

(8)

where Profiti,t is a modified version of log profits, namely sign(profits)*log(1+|profits|) to allow for

negative values, realized by firm ion trading day t, Volumei,s is the log of each traders trading volume


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for that day; Volatilitys is the price volatility of that day defined as the (volume-weighted) standard

deviation of the price process throughout that trading day; and Aggressivenessi,s is trader i's average

(volume-weighted) aggressiveness ratio. We include these regressors to control for both time-specific

and firm-specific effects.

The results are reported in Table 6, Panel A.


Columns 1, 3, and 5 are coefficients with the standard errors in the column to the right. Columns 1 3

are univariate regressions, while Columns 4 6 include the control variables. The univariate results for

each type of HFT show that one-day lagged performance is a predictor of todays performance.

Similarly, the specification with control variables maintains the statistical significance, demonstrating

that profitability is persistent even after controlling for time effects.

It may be that persistence is strongest for the best performing firms, the idea being that the best

performing firms not only are the best in that they earn the highest profits, but also that they do so

regularly. To test this we rerun the OLS regression specified in Equation 8, but include a dummy

variable 1Top 3rd i,t-1 to capture top performing firms. 1Top 3rd i,t-1 is a dummy variable taking the value one if

firm ion dayt-1 was in the top one-third of its profitability among its subgroup of HFT firms. We thus

repeat the OLS analysis and report the results in Table 6, Panel A, Columns 7 9. The coefficient on

the top one-third dummy is not statistically significant. Thus, we conclude that persistence in profits is

a common feature among HFT firms, it is not being driven only by the best performing firms.

We repeat the OLS analysis and report the results in Table 6, Panel A, Columns 7 9. The

coefficient on the top one-third dummy is not statistically significant. Thus, we conclude that


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persistence in profits is a common feature among HFT firms, it is not being driven only by the best

performing firms.

Panel A tests whether a firms profits yesterday predict its profits today. Panel B does the same

but at longer horizons, from one month up to one year. Panel B repeats the analysis in the last

specification but replaces the 1-day lag value of profits and the 1-day lag top one-third dummy with the

profit from an earlier period: one-month earlier, two months earlier, six months earlier, and one year

earlier. Each coefficient is obtained by running the full specification regression from Panel A (Columns

7 9) but replace the lag of profitability from 1 day to longer horizons, between 30 days and one year.

Each Column in Panel A is a different regression. The dependent variability is Profitability of firm i on

day t, and the HFT firms are analyzed in separate subcategories: Aggressive, Mixed, and Passive.

The results show that persistence in Aggressive HFT dies out quickly; after 30-days it is no

longer statistically significant. However, for Mixed and Passive the persistence lasts, for half a year for

Mixed firms and for two months for Passive firms.

b. New HFT FirmsPersistent profit is one piece of evidence suggesting that HFT profits are gained by more than

just luck. However, the persistence of profits cannot distinguish what drives the high profits. We

consider two factors that may influence profitability: newness and speed. We expect, given the high

Sharpe ratios observed in Section III that new entrants would try and capture market share. If success

in HFT is independent of ability or newness, we would expect new firms to perform in line with more

experience firms. To analyze this hypothesis we look at trading profits again, but focus now on new

entrants. We repeat a similar regression as in Equation 8:

. (9)


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The control variables are the same as in Table 6. Lagged Profits is excluded as a control as it may

confound with the variable of interest, the dummy variable, New Entrant i,t, which takes the value 1

during a period after a new HFT firm participates in the market. We consider four different time

periods for a firm to be considered a new entrant: 1 month, 2, 3, and 4 months after first appearing as

an HFT. So the < 1 month olddummy variable will take the value one for firm iduring t to t + 30 if firm

ibegan trading on dayt-1, otherwise it will take the value zero. We exclude the observations in 2010 as

this is when we first observe any firm. Every two rows represent three regressions for a subgroup of

HFT: Aggressive, Mixed, and Passive. The two, three, and four month dummy variables are similarly

defined. The results are reported in Table 7, Panel A.


The coefficients are reported in Columns 1, 3, and 5; their robust standard errors are reported in

Columns 2, 4, and 6. Each regression includes the full set of control variables identified above. The

Adjusted R-square is reported below the coefficient.

The regressions for the new entrants for less than one month are statistically insignificant except

for Mixed HFT, which has a positive coefficient, suggesting that new Mixed HFT entrants earn more

profits than HFTs with a longer track record. When looking longer, at 2-months, the Mixed HFT

statistical significance disappears, but Passive HFT new entrants now have a positive coefficient.

However, the three and four month definition show that new Aggressive HFTs and new Passive HFTs

underperform. These results suggest that, immediately, new HFT entrants are not at a disadvantage,

and may outperform, but that after their initial entry, as soon as three or four months after, they began

to underperform. If HFTs need to continually adapt and update their algorithms, it could be that new

entrants start with competitive algorithms but are less able to keep up with technological change.


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The limitation of the above analysis is that it does not take into account exit. That is, a new HFT

firm that is performing poorly may choose to exit trading, and hence the data set. Thus we may have

survival bias - if a firm drops out of the dataset, it will likely do so because of poor performance, but

then we are missing observations that would suggest that new entrants underperform even more.

Consequently we may be over-estimating the performance of new entrants. To address the

survival issue, we perform a Logit regression to determine whether new entrants are more likely to exit:

(10)

where Exiti,t takes the value 1 on day t for firm i if that is the last day firm i trades. The

coefficient of interest is again the dummy variable,New Entrant i,t, defined as above. In addition to the

excluded observations described in Panel A, this regression excludes observations in August 2012, the

last month of the analysis, due to this being the last month of the data set. The control variables are as

defined above. The results are reported in Table 7, Panel B. The coefficients are reported in Columns 1,

3, and 5; their robust standard errors are reported in Columns 2, 4, and 6. Each regression includes the

full set of control variables identified above. The Pseudo R-square is reported below the coefficient.

For Aggressive and Mixed HFT new entrants, regardless of the time horizon of the definition,

are much more likely to stop trading than their more experienced competitors. We speculate that new

entrants having a difficult time surviving will limit the degree to which competitive forces may drive

down the profits of existing HFTs.

We are careful not to conclude that experience drives profitability. Alternatively, the higher

profitability of established HFTs could be due to a survivorship bias: profitable firms remain while

unprofitable firms exit; this process of selection results in established firms having a higher average

profitability than entrants, who have not been selected out. Thus, we can conclude that something other

than chance determines firms profits, but cannot say whether it is experience or a survivorship bias.


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c. SpeedFinally, we look at the relationship between speed and profits and show that there is an

association between the two. Our measure of latency is similar to Wellers (2012): we measure latency

of a firm as the 5th percentile of the duration between switching from a passive trade to an aggressive

trade, measured in milliseconds. While this measure may not be suitable for every HFT, such as HFTs

that trade all passively or all aggressively, it is a way to capture an active decision that is likely a

response to market events. In contrast to other measures such as the duration between switching from

an aggressive buy to an aggressive sell, which may suggest more about the timing ofa firms inventory

management strategies, our latency measure aims to capture a firms reaction speed to market events

given its technological constraint.

We sort Aggressive/Mixed HFTs and Passive HFTs firm-day observations into decile bins

corresponding to their latency, and then take the average of both the latency and the profits over all

firm-day observations within each decile bin.15Speed is the reciprocal of the average latency (plus 1

millisecond, to ensure we do not divide by zero). Figure 6 plotsSpeedvs. average profits for each decile

bin.


Panel A showsSpeedvs. average profits for Aggressive and Mixed HFTs (grouped together), and

Panel B shows the same for Passive HFTs. The three lines trace the relationship between speed and

profits at approximately one-year intervals (October 2010, July 2011, August 2012).16 Figure 6 suggests

a positive relationship between profits and Speed. In the months examined, there is a roughly

increasing relationship between profits andSpeed.

15Firm-day profit observations which resulted in gains or losses of over $100,000 were considered outliers and

excluded in producing Figure 6.16 Because millisecond time stamps were needed for this analysis, we were limited to which months we could look at.


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The graphs, which trace the relationship between Speedand profits at approximately one-year

intervals (October 2010, July 2011, August 2012), show thatSpeedis increasing over the two-year span.

Between October 2010, July 2011 and August 2012, the average Speedof the top decile increases from

approximately 0.4 to 0.75 to 1; similarly, the speed of the second-to-top decile increases from

approximately 0.27 to 0.32 to 1. There are similar increases inSpeedfor Passive HFTs. AlthoughSpeed

increases over the two-year span, average profit fluctuates month-to-month with no clear trend over

time. That HFT speed increases over time while the distribution of profits is relatively stable leads us to

ask whether HFT profitability is associated with relative or absolute profits.

We estimate the following regression from firm-day observations of HFT profitability:

(11)

whereProfits,i,tis again a modified version of log profits, namely sign(profits)*log(1+|profits|) to allow

for negative values,AbsoluteSpeedi,tis the speed measure described above,RelativeSpeedi,tis the firm's

ranking that day in terms of speed among all firms of that sub-type scaled by the total number of firms

that day of that sub-type. The control variables used are the same as before: the HFTs aggressiveness,

the days total trading volume, and the days price volatility. The results are reported in Table 8.


Table 8 shows that for all three sub-types of HFTs, profits are increasing in both in absolute

speed, with statistically significant coefficients of 14.44, 12.72 and 6.15 for Aggressive, Mixed, and

Passive HFTs respectively, and in relative speed, with statistically significant coefficients of -6.72, -4.44

and -2.62 for Aggressive, Mixed, and Passive HFTs respectively. The signs of the coefficients are as one

would expect: profits are increasing with absolute speed but decreasing in relative speed (higher

relative rank means higher profits). However, after combining the two regressors together and adding


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controls, only Absolute Speed is statistically significant for Aggressive HFTs, only Relative Speed is

statistically significant for Mixed HFTs, and neither of the regressors is statistically significant for

Passive HFTs.

VI. Conclusion

Using data that identify individual firms, this paper examines the profitability of HFTs. This

paper has three key findings. First, HFT is highly profitable (before incorporating operating and trading

costs) but not without risks. The magnitude and consistency of their profits as well as their risk-return

tradeoff demonstrate unusually strong performance. Second, HFTs are a heterogeneous set of firms

that have different trading and profit characteristics. Third, we describe different market conditions

and firm characteristics that are associated with profitability, such as aggressiveness, speed, and

newness. Our findings shed light on the competitiveness of the HFT industry and provide insight into

the determinants of HFT profitability.


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References

Ackermann, C., R. McEnally, and D. Ravenscraft, 1999. The performance of hedge funds: Risk, return,and incentives,Journal of Finance, 54 (3), 833-874.

Anand, A., P. Irvine, A. Puckett, and K. Venkataraman, 2012, Performance of institutional tradingdesks: An analysis of persistence in trading costs,Review of Financial Studies, 25 (2), 557-598.

Badrinath, S., J. Kale, and T. Noe, 1995, Of shepherds, sheep, and the cross-autocorrelations in equityreturns,Review of Financial Studies, 8 (2), 401-430.

Barber, B., T. Odean, and N. Zhu, 2009, Do retail trades move markets? Review of Financial Studies,22 (1), 151-186.

Boehmer, E. and J. Wu, 2008. Order flow and prices. Working Paper.

Boulatov, A., T. Hendershott, and D. Livdan, 2011, Informed trading and portfolio returns, Review ofEconomic Studies, Forthcoming.

Brogaard, J., T. Hendershott, and R. Riordan, 2011, High frequency trading and price discovery,Working Paper.

Carhart, M., 1997, On persistence in mutual fund performance,Journal of Finance, 52 (1), 57-82.

Coughenour, J. and M. Saad, 2004, Common market makers and commonality in liquidity, Journal ofFinancial Economics, 73 (1), 37-69.

Easley, D. and M. OHara, 1987, Price, trade size, and information in securities markets, Journal ofFinancial Economics, 19 (1), 69-90.

Fama, E. and K. French, 2002, The equity premium,Journal of Finance, 57 (2), 637-659.

Frank, R., 2005, Positional externalities cause large and preventable welfare losses, AmericanEconomic Review, 95 (2), 137141.

Glosten, L., and P. Milgrom, 1985, Bid, ask and transaction prices in a specialist market withheterogeneously informed traders,Journal of Financial Economics, 14 (1), 71-100.

Grinblatt, M. and M. Keloharju, 2001, What makes investors trade?, Journal of Finance, 56 (2), 589-616.

Grinblatt, M., M. Keloharju, and J. Linnainmaa, 2011, IQ, trading behavior, and performance, Journalof Financial Economics, 104 (2), 339-362.

Grossman, S. and J. Stiglitz, 1980, On the impossibility of informationally efficient markets, American

Economic Review, 70 (3), 393-408.

Harris, J. and P. Schultz, 1998, The trading profits of soes bandits,Journal of Financial Economics, 50(1), 39-62.

Hasbrouck, J., 2003, Intraday price formation in US equity index markets,Journal of Finance, 58 (6),2375-2400.

Hasbrouck, J. and G. Saar, 2010, Low-latency trading, Working Paper.


38/57

Hasbrouck, J. and G. Sofianos, 1993, The trades of market makers: An empirical analysis of NYSEspecialists,Journal of Finance, 48 (5), 1565-1593.

Hendershott, T., D. Livdan, and N. Schurhoff, 2012, Are institutions informed about news?, WorkingPaper.

Hendershott, T., and R. Riordan, 2009, Algorithmic trading and information, Working Paper.Hirshleifer, J., 1971, The private and social value of information and the reward to inventive activity,

American Economic Review, 61 (4), 561-574.

Heston, S., R. Korajczyk, and R. Sadka, 2010, Intraday patterns in the cross-section of stock returns,Journal of Finance, 65 (4), 1369-1407.

Hirschey, N., 2011, Do high-frequency traders anticipate buying and selling pressure?, Working Paper.

Hvidkjaer, S., 2008, Small trades and the cross-section of stock returns,Review of Financial Studies, 21(3), 1123-1151.

Jagannathan, R., A. Malakhov, and D. Novikov, 2010, Do hot hands exist among hedge fund managers?an empirical evaluation,Journal of Finance, 65 (1), 217-255.

Kaniel, R., G. Saar, and S. Titman, 2008, Individual investor trading and stock returns, Journal ofFinance, 63 (1), 273-310.

Karlin and Taylor, 1975.A first course in stochastic processes, 2nd edition New York: Academic Press.

Kirilenko, A., A. Kyle, M. Samadi, and T. Tuzun, 2010, The flash crash: The impact of high frequencytrading on an electronic market, Working Paper.

Kyle, A., 1985, Continuous auctions and insider trading,Econometrica, 53 (6), 1315-1335.

Lazear, E., and S. Rosen, 1981, Rank-order tournaments as optimum labor contracts, Journal of

Political Economy, 89 (5), 841-64,

Menkveld, A., 2011, High frequency trading and the new-market makers, Working Paper.

Puckett, A., and X. Yan, 2011, The interim trading skills of institutional investors, Journal of Finance,66 (2), 601-633.

Seasholes, M., and N. Zhu, 2010, Individual investors and local bias,Journal of Finance, 65 (5), 1987-2010.

Sharpe, W,. 1966, Mutual fund performance,Journal of Business, 39 (1), 119-138.

Seru, A., T. Shumway, and N. Stoffman, 2010, Learning by trading,Review of Financial Studies, 23 (2),

705-739.

Weller, B., 2012, Liquidity and High Frequency Trading, Working Paper.


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Figure 1 HFT Activity

Panel A shows the average daily HFT volume of all HFT accounts combined. Panel B looks at whatpercent of market volume each trader type comprises. Panel C looks at the absolute value end-of-dayposition averaged across firms. Panel D looks at the intraday inventory range (max intraday position min intraday position) averaged across firms.

Panel A: Percent market volume of all trader types

Panel B: HFT average daily volume

0.00

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HFTa HFTm HFTp

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HFTa HFTm HFTp MM fund opp small


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Panel C: Absolute value end-of-day position averaged over all firms

Panel D: Intraday inventory range (max intraday position min intraday position) averaged overall firms

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[Max intraday position - Min intraday position]average over all firms

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Figure 2. Profits Time Series

This Figure shows the time-series of average daily HFT profits (Panel A) and profits per contract (PanelB), broken down into Aggressive, Mixed and Passive groups and with all firms aggregated together intheir respective groups.

Panel A: Profits

Panel B: Profits per Contract

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Figure 3. Profits Distribution

This Figure plots the average daily profits of firms at the 10th, 25th, 50th, 75th and 90th percentiles. Eachpanel is broken down into three graphs for Aggressive, Mixed and Passive HFTs.

Panel A: Profits

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HFTA profits: distribution across accounts

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HFTp p10 HFTp p25 HFTp p50 HFTp p75 HFTp p90


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Panel B: Profits per Contract

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baron brogaard kirilenko

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